Papers › Simple Approximative Algorithms for Free-Support Wasserstein Barycenters
Simple Approximative Algorithms for Free-Support Wasserstein Barycenters
Johannes von Lindheim
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative algorithms. In this paper, we analyze a well-known simple framework for approximating Wasserstein-p barycenters, where we mainly consider the most common case p=2 and p=1, which is not as well discussed. The framework produces sparse support solutions and shows good numerical results in the free-support setting. Depending on the desired level of accuracy, this requires only N-1 or N(N-1)/2 standard two-marginal optimal transport (OT) computations between the N input measures, respectively, which is fast, memory-efficient and easy to implement using any OT solver as a black box. What is more, these methods yield a relative error of at most N and $2$, respectively, for both p=1, 2. We show that these bounds are practically sharp. In light of the hardness of the problem, it is not surprising that such guarantees cannot be close to optimality in general. Nevertheless, these error bounds usually turn out to be drastically lower for a given particular problem in practice and can be evaluated with almost no computational overhead, in particular without knowledge of the optimal solution. In our numerical experiments, this guaranteed errors of at most a few percent.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections